p-Eigenvalue pinching sphere theorems
Abstract
In this paper, we establish two p -eigenvalue pinching sphere theorems, for the p -Laplacian, p > 1. The first result states that if the first non-zero p -eigenvalue of a closed Riemannian n -manifold with sectional curvature K M ≥ 1 is sufficiently close to the first non-zero p -eigenvalue of S n then M is homeomorphic to S n . The second states that if the first non-zero p -eigenvalue of a closed Riemannian n -manifold with Ricci curvature R i c M ≥ ( n − 1 ) and injectivity radius inj M ≥ i 0 > 0 is sufficiently close to the first non-zero p -eigenvalue of S n then M is diffeomorphic to S n . Our results extend sphere theorems originally settled for the Laplacian by S. Croke [1] and G.P. Bessa [2] respectively.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Geometry and complex manifolds
Publication details
- Journal / source
- Nonlinear Analysis
- Publisher
- Elsevier BV
- Volume
- 267
- Pages
- 114056–114056
- Publication date
- 20 January 2026
- Language
- EN